The relationship between convolutional structure and equivariance has been long known in algebraic signal processing theory [1]}. Recently, necessity results have re-gained attention in the context of neural network architecture design [2]}. Several Group Convolutional neural network architectures that generalize CNNs to different groups by leveraging group convolutions have been proposed [3]}, [4]}, [5]}. In the case of images, it has been shown that that SE2 equivariant layers can be implemented efficiently using regular 2D convolutions [6]}. This approach allows to derive a parametrization for CNN filters under finite subgroups of SE2. Among other works [7]}, [8]} give theoretical analyses of the benefits of group invariance in learning settings.
